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<div class="title">EigenSolver.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2010,2012 Jitse Niesen &lt;jitse@maths.leeds.ac.uk&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_EIGENSOLVER_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_EIGENSOLVER_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./RealSchur.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html">   66</a></span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">class </span><a class="code" href="classEigen_1_1EigenSolver.html">EigenSolver</a></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;{</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">   71</a></span>&#160;    <span class="keyword">typedef</span> MatrixType_ <a class="code" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">MatrixType</a>;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;      RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;      ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;      Options = MatrixType::Options,</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    };</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a066f584d04b0b8ef1411e3eea9cda7f2">   82</a></span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code" href="classEigen_1_1EigenSolver.html#a066f584d04b0b8ef1411e3eea9cda7f2">Scalar</a>;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> RealScalar;</div>
<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">   84</a></span>&#160;    <span class="keyword">typedef</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a> <a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a>; </div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160; </div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a789af79c9427e6617fa8cbd96a6a258e">   92</a></span>&#160;    <span class="keyword">typedef</span> std::complex&lt;RealScalar&gt; <a class="code" href="classEigen_1_1EigenSolver.html#a789af79c9427e6617fa8cbd96a6a258e">ComplexScalar</a>;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a97733b9f7b4a2cc4496d4066e320c50c">   99</a></span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;ComplexScalar, ColsAtCompileTime, 1, Options &amp; ~RowMajor, MaxColsAtCompileTime, 1&gt;</a> <a class="code" href="classEigen_1_1EigenSolver.html#a97733b9f7b4a2cc4496d4066e320c50c">EigenvalueType</a>;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#ae1f52c25907e5f00abe236be002eeb89">  106</a></span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime&gt;</a> <a class="code" href="classEigen_1_1EigenSolver.html#ae1f52c25907e5f00abe236be002eeb89">EigenvectorsType</a>;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a85cf52711e7100b01fda3e329eb86e5e">  115</a></span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html#a85cf52711e7100b01fda3e329eb86e5e">EigenSolver</a>() : m_eivec(), m_eivalues(), m_isInitialized(false), m_eigenvectorsOk(false), m_realSchur(), m_matT(), m_tmp() {}</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a311f148c5d12ecda1eec61e31ea8c3ed">  123</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1EigenSolver.html#a311f148c5d12ecda1eec61e31ea8c3ed">EigenSolver</a>(<a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> size)</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;      : m_eivec(size, size),</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        m_eivalues(size),</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        m_isInitialized(false),</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        m_eigenvectorsOk(false),</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        m_realSchur(size),</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        m_matT(size, size), </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        m_tmp(size)</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    {}</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160; </div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00149"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a0ccaeb4f7d44c18af60a7b3a1dd91f7a">  149</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1EigenSolver.html#a0ccaeb4f7d44c18af60a7b3a1dd91f7a">EigenSolver</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix, <span class="keywordtype">bool</span> computeEigenvectors = <span class="keyword">true</span>)</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;      : m_eivec(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;        m_eivalues(matrix.cols()),</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;        m_isInitialized(false),</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        m_eigenvectorsOk(false),</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        m_realSchur(matrix.cols()),</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        m_matT(matrix.rows(), matrix.cols()), </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        m_tmp(matrix.cols())</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    {</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;      <a class="code" href="classEigen_1_1EigenSolver.html#a9e03d09fd7cfc0120847fcb63aa353f3">compute</a>(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>(), computeEigenvectors);</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    }</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160; </div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html#ae1f52c25907e5f00abe236be002eeb89">EigenvectorsType</a> <a class="code" href="classEigen_1_1EigenSolver.html#a66288022802172e3ee059283b26201d7">eigenvectors</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160; </div>
<div class="line"><a name="l00201"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#ac306853588d05e71d5c0f883d37327f2">  201</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">MatrixType</a>&amp; <a class="code" href="classEigen_1_1EigenSolver.html#ac306853588d05e71d5c0f883d37327f2">pseudoEigenvectors</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;EigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;      eigen_assert(m_eigenvectorsOk &amp;&amp; <span class="stringliteral">&quot;The eigenvectors have not been computed together with the eigenvalues.&quot;</span>);</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;      <span class="keywordflow">return</span> m_eivec;</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    }</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160; </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">MatrixType</a> <a class="code" href="classEigen_1_1EigenSolver.html#a4979eafe0aeef06b19ada7fa5e19db17">pseudoEigenvalueMatrix</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160; </div>
<div class="line"><a name="l00246"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a0f507ad7ab14797882f474ca8f2773e7">  246</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">EigenvalueType</a>&amp; <a class="code" href="classEigen_1_1EigenSolver.html#a0f507ad7ab14797882f474ca8f2773e7">eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;EigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;      <span class="keywordflow">return</span> m_eivalues;</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;    }</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160; </div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00280"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a9e03d09fd7cfc0120847fcb63aa353f3">  280</a></span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html">EigenSolver</a>&amp; <a class="code" href="classEigen_1_1EigenSolver.html#a9e03d09fd7cfc0120847fcb63aa353f3">compute</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix, <span class="keywordtype">bool</span> computeEigenvectors = <span class="keyword">true</span>);</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a5c28d646d456a22a2726f49e4e5e8536">  283</a></span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code" href="classEigen_1_1EigenSolver.html#a5c28d646d456a22a2726f49e4e5e8536">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;EigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;      <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    }</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160; </div>
<div class="line"><a name="l00290"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a5fbbdf49cf33b52b1c581bf06319bb91">  290</a></span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html">EigenSolver</a>&amp; <a class="code" href="classEigen_1_1EigenSolver.html#a5fbbdf49cf33b52b1c581bf06319bb91">setMaxIterations</a>(<a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> maxIters)</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    {</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;      m_realSchur.<a class="code" href="classEigen_1_1RealSchur.html#a10f9307a8dc2259c86e6dba0edbde308">setMaxIterations</a>(maxIters);</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    }</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160; </div>
<div class="line"><a name="l00297"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#acfebb3f08831cb923511dad5a6e78401">  297</a></span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> <a class="code" href="classEigen_1_1EigenSolver.html#acfebb3f08831cb923511dad5a6e78401">getMaxIterations</a>()</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    {</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;      <span class="keywordflow">return</span> m_realSchur.<a class="code" href="classEigen_1_1RealSchur.html#a57eea8f6a25be4ac710097fd6cce9366">getMaxIterations</a>();</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;    }</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160; </div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    <span class="keywordtype">void</span> doComputeEigenvectors();</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160; </div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    </div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">void</span> check_template_parameters()</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    {</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;      EIGEN_STATIC_ASSERT_NON_INTEGER(<a class="code" href="classEigen_1_1EigenSolver.html#a066f584d04b0b8ef1411e3eea9cda7f2">Scalar</a>);</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;      EIGEN_STATIC_ASSERT(!<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::IsComplex</a>, NUMERIC_TYPE_MUST_BE_REAL);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    }</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    </div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">MatrixType</a> m_eivec;</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html#a97733b9f7b4a2cc4496d4066e320c50c">EigenvalueType</a> m_eivalues;</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    <span class="keywordtype">bool</span> m_eigenvectorsOk;</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    RealSchur&lt;MatrixType&gt; m_realSchur;</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    <a class="code" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">MatrixType</a> m_matT;</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160; </div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="keyword">typedef</span> Matrix&lt;Scalar, ColsAtCompileTime, 1, Options &amp; ~RowMajor, MaxColsAtCompileTime, 1&gt; ColumnVectorType;</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    ColumnVectorType m_tmp;</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;};</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160; </div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00326"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a4979eafe0aeef06b19ada7fa5e19db17">  326</a></span>&#160;<a class="code" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">MatrixType</a> <a class="code" href="classEigen_1_1EigenSolver.html#a4979eafe0aeef06b19ada7fa5e19db17">EigenSolver&lt;MatrixType&gt;::pseudoEigenvalueMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;EigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  <span class="keyword">const</span> RealScalar precision = RealScalar(2)*<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;RealScalar&gt;::epsilon</a>();</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  <a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> n = m_eivalues.rows();</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  <a class="code" href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">MatrixType</a> matD = MatrixType::Zero(n,n);</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> i=0; i&lt;n; ++i)</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  {</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    <span class="keywordflow">if</span> (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i)), precision))</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;      matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;    {</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;      matD.template block&lt;2,2&gt;(i,i) &lt;&lt;  numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;                                       -numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;      ++i;</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    }</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  }</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  <span class="keywordflow">return</span> matD;</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;}</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160; </div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00347"></a><span class="lineno"><a class="line" href="classEigen_1_1EigenSolver.html#a66288022802172e3ee059283b26201d7">  347</a></span>&#160;<span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">EigenSolver&lt;MatrixType&gt;::EigenvectorsType</a> <a class="code" href="classEigen_1_1EigenSolver.html#a66288022802172e3ee059283b26201d7">EigenSolver&lt;MatrixType&gt;::eigenvectors</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;EigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  eigen_assert(m_eigenvectorsOk &amp;&amp; <span class="stringliteral">&quot;The eigenvectors have not been computed together with the eigenvalues.&quot;</span>);</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  <span class="keyword">const</span> RealScalar precision = RealScalar(2)*<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;RealScalar&gt;::epsilon</a>();</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  <a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> n = m_eivec.cols();</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  <a class="code" href="classEigen_1_1Matrix.html">EigenvectorsType</a> matV(n,n);</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> j=0; j&lt;n; ++j)</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  {</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    <span class="keywordflow">if</span> (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j)), precision) || j+1==n)</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    {</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;      <span class="comment">// we have a real eigen value</span></div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;      matV.col(j) = m_eivec.col(j).template cast&lt;ComplexScalar&gt;();</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;      matV.col(j).normalize();</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    }</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    {</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;      <span class="comment">// we have a pair of complex eigen values</span></div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Index</a> i=0; i&lt;n; ++i)</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;      {</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;        matV.<a class="code" href="classEigen_1_1PlainObjectBase.html#a992d58b5453e441dcfc80f21c2bfd1d7">coeffRef</a>(i,j)   = <a class="code" href="classEigen_1_1EigenSolver.html#a789af79c9427e6617fa8cbd96a6a258e">ComplexScalar</a>(m_eivec.coeff(i,j),  m_eivec.coeff(i,j+1));</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;        matV.<a class="code" href="classEigen_1_1PlainObjectBase.html#a992d58b5453e441dcfc80f21c2bfd1d7">coeffRef</a>(i,j+1) = <a class="code" href="classEigen_1_1EigenSolver.html#a789af79c9427e6617fa8cbd96a6a258e">ComplexScalar</a>(m_eivec.coeff(i,j), -m_eivec.coeff(i,j+1));</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;      }</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;      matV.col(j).normalize();</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;      matV.col(j+1).normalize();</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;      ++j;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;    }</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  }</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  <span class="keywordflow">return</span> matV;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;}</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160; </div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<a class="code" href="classEigen_1_1EigenSolver.html">EigenSolver&lt;MatrixType&gt;</a>&amp; </div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;<a class="code" href="classEigen_1_1EigenSolver.html#a9e03d09fd7cfc0120847fcb63aa353f3">EigenSolver&lt;MatrixType&gt;::compute</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix, <span class="keywordtype">bool</span> computeEigenvectors)</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;{</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;  check_template_parameters();</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;  </div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  <span class="keyword">using</span> numext::isfinite;</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;  eigen_assert(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>() == matrix.<a class="code" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>());</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160; </div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  <span class="comment">// Reduce to real Schur form.</span></div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  m_realSchur.compute(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>(), computeEigenvectors);</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;  </div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;  m_info = m_realSchur.info();</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160; </div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  <span class="keywordflow">if</span> (m_info == <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>)</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;  {</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    m_matT = m_realSchur.matrixT();</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    <span class="keywordflow">if</span> (computeEigenvectors)</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;      m_eivec = m_realSchur.matrixU();</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;  </div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    <span class="comment">// Compute eigenvalues from matT</span></div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    m_eivalues.resize(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>());</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0;</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    <span class="keywordflow">while</span> (i &lt; matrix.<a class="code" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>()) </div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    {</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;      <span class="keywordflow">if</span> (i == matrix.<a class="code" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>() - 1 || m_matT.coeff(i+1, i) == Scalar(0)) </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;      {</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;        m_eivalues.coeffRef(i) = m_matT.coeff(i, i);</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;        <span class="keywordflow">if</span>(!(<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(m_eivalues.coeffRef(i)))</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;        {</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;          m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;          m_eigenvectorsOk = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;          m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">NumericalIssue</a>;</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;          <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;        }</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;        ++i;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;      }</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;      {</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;        Scalar p = Scalar(0.5) * (m_matT.coeff(i, i) - m_matT.coeff(i+1, i+1));</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;        Scalar z;</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        <span class="comment">// Compute z = sqrt(abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));</span></div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;        <span class="comment">// without overflow</span></div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;        {</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;          Scalar t0 = m_matT.coeff(i+1, i);</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;          Scalar t1 = m_matT.coeff(i, i+1);</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;          Scalar maxval = numext::maxi&lt;Scalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(p),numext::maxi&lt;Scalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(t0),<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(t1)));</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;          t0 /= maxval;</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;          t1 /= maxval;</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;          Scalar p0 = p/maxval;</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;          z = maxval * <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(p0 * p0 + t0 * t1));</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;        }</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;        </div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;        m_eivalues.coeffRef(i)   = ComplexScalar(m_matT.coeff(i+1, i+1) + p, z);</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;        m_eivalues.coeffRef(i+1) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, -z);</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;        <span class="keywordflow">if</span>(!((<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(m_eivalues.coeffRef(i)) &amp;&amp; (<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(m_eivalues.coeffRef(i+1))))</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;        {</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;          m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;          m_eigenvectorsOk = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;          m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">NumericalIssue</a>;</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;          <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;        }</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;        i += 2;</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;      }</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    }</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    </div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    <span class="comment">// Compute eigenvectors.</span></div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;    <span class="keywordflow">if</span> (computeEigenvectors)</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;      doComputeEigenvectors();</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  }</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160; </div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;  m_eigenvectorsOk = computeEigenvectors;</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160; </div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;}</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160; </div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160; </div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;<span class="keywordtype">void</span> EigenSolver&lt;MatrixType&gt;::doComputeEigenvectors()</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;{</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size = m_eivec.cols();</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;  <span class="keyword">const</span> Scalar eps = NumTraits&lt;Scalar&gt;::epsilon();</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160; </div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  <span class="comment">// inefficient! this is already computed in RealSchur</span></div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;  Scalar norm(0);</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; size; ++j)</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;  {</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;    norm += m_matT.row(j).segment((std::max)(j-1,<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>(0)), size-(std::max)(j-1,<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>(0))).cwiseAbs().sum();</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;  }</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;  </div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  <span class="comment">// Backsubstitute to find vectors of upper triangular form</span></div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;  <span class="keywordflow">if</span> (norm == Scalar(0))</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  {</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;  }</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160; </div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = size-1; n &gt;= 0; n--)</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  {</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    Scalar p = m_eivalues.coeff(n).real();</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;    Scalar q = m_eivalues.coeff(n).imag();</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160; </div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;    <span class="comment">// Scalar vector</span></div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;    <span class="keywordflow">if</span> (q == Scalar(0))</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    {</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;      Scalar lastr(0), lastw(0);</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> l = n;</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160; </div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;      m_matT.coeffRef(n,n) = Scalar(1);</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = n-1; i &gt;= 0; i--)</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;      {</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;        Scalar w = m_matT.coeff(i,i) - p;</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;        Scalar r = m_matT.row(i).segment(l,n-l+1).dot(m_matT.col(n).segment(l, n-l+1));</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160; </div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;        <span class="keywordflow">if</span> (m_eivalues.coeff(i).imag() &lt; Scalar(0))</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;        {</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;          lastw = w;</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;          lastr = r;</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;        }</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;        {</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;          l = i;</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;          <span class="keywordflow">if</span> (m_eivalues.coeff(i).imag() == Scalar(0))</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;          {</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;            <span class="keywordflow">if</span> (w != Scalar(0))</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;              m_matT.coeffRef(i,n) = -r / w;</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;            <span class="keywordflow">else</span></div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;              m_matT.coeffRef(i,n) = -r / (eps * norm);</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;          }</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;          <span class="keywordflow">else</span> <span class="comment">// Solve real equations</span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;          {</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;            Scalar x = m_matT.coeff(i,i+1);</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;            Scalar y = m_matT.coeff(i+1,i);</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;            Scalar denom = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;            Scalar t = (x * lastr - lastw * r) / denom;</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;            m_matT.coeffRef(i,n) = t;</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;            <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(x) &gt; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(lastw))</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;              m_matT.coeffRef(i+1,n) = (-r - w * t) / x;</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;            <span class="keywordflow">else</span></div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;              m_matT.coeffRef(i+1,n) = (-lastr - y * t) / lastw;</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;          }</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160; </div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;          <span class="comment">// Overflow control</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;          Scalar t = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_matT.coeff(i,n));</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;          <span class="keywordflow">if</span> ((eps * t) * t &gt; Scalar(1))</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;            m_matT.col(n).tail(size-i) /= t;</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;        }</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;      }</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;    }</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (q &lt; Scalar(0) &amp;&amp; n &gt; 0) <span class="comment">// Complex vector</span></div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;    {</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;      Scalar lastra(0), lastsa(0), lastw(0);</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> l = n-1;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160; </div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;      <span class="comment">// Last vector component imaginary so matrix is triangular</span></div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;      <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_matT.coeff(n,n-1)) &gt; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_matT.coeff(n-1,n)))</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;      {</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;        m_matT.coeffRef(n-1,n-1) = q / m_matT.coeff(n,n-1);</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;        m_matT.coeffRef(n-1,n) = -(m_matT.coeff(n,n) - p) / m_matT.coeff(n,n-1);</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;      }</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;      {</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;        ComplexScalar cc = ComplexScalar(Scalar(0),-m_matT.coeff(n-1,n)) / ComplexScalar(m_matT.coeff(n-1,n-1)-p,q);</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;        m_matT.coeffRef(n-1,n-1) = numext::real(cc);</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;        m_matT.coeffRef(n-1,n) = numext::imag(cc);</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;      }</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;      m_matT.coeffRef(n,n-1) = Scalar(0);</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;      m_matT.coeffRef(n,n) = Scalar(1);</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = n-2; i &gt;= 0; i--)</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;      {</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;        Scalar ra = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n-1).segment(l, n-l+1));</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;        Scalar sa = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n).segment(l, n-l+1));</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;        Scalar w = m_matT.coeff(i,i) - p;</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160; </div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;        <span class="keywordflow">if</span> (m_eivalues.coeff(i).imag() &lt; Scalar(0))</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;        {</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;          lastw = w;</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;          lastra = ra;</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;          lastsa = sa;</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;        }</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;        {</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;          l = i;</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;          <span class="keywordflow">if</span> (m_eivalues.coeff(i).imag() == RealScalar(0))</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;          {</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;            ComplexScalar cc = ComplexScalar(-ra,-sa) / ComplexScalar(w,q);</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;            m_matT.coeffRef(i,n-1) = numext::real(cc);</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;            m_matT.coeffRef(i,n) = numext::imag(cc);</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;          }</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;          <span class="keywordflow">else</span></div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;          {</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;            <span class="comment">// Solve complex equations</span></div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;            Scalar x = m_matT.coeff(i,i+1);</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;            Scalar y = m_matT.coeff(i+1,i);</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;            Scalar vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;            Scalar vi = (m_eivalues.coeff(i).real() - p) * Scalar(2) * q;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;            <span class="keywordflow">if</span> ((vr == Scalar(0)) &amp;&amp; (vi == Scalar(0)))</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;              vr = eps * norm * (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(w) + <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(q) + <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(x) + <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(y) + <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(lastw));</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160; </div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;            ComplexScalar cc = ComplexScalar(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra) / ComplexScalar(vr,vi);</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;            m_matT.coeffRef(i,n-1) = numext::real(cc);</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;            m_matT.coeffRef(i,n) = numext::imag(cc);</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;            <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(x) &gt; (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(lastw) + <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(q)))</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;            {</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;              m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;              m_matT.coeffRef(i+1,n) = (-sa - w * m_matT.coeff(i,n) - q * m_matT.coeff(i,n-1)) / x;</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;            }</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;            <span class="keywordflow">else</span></div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;            {</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;              cc = ComplexScalar(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n)) / ComplexScalar(lastw,q);</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;              m_matT.coeffRef(i+1,n-1) = numext::real(cc);</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;              m_matT.coeffRef(i+1,n) = numext::imag(cc);</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;            }</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;          }</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160; </div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;          <span class="comment">// Overflow control</span></div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;          Scalar t = numext::maxi&lt;Scalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_matT.coeff(i,n-1)),<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_matT.coeff(i,n)));</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;          <span class="keywordflow">if</span> ((eps * t) * t &gt; Scalar(1))</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;            m_matT.block(i, n-1, size-i, 2) /= t;</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160; </div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;        }</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;      }</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;      </div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;      <span class="comment">// We handled a pair of complex conjugate eigenvalues, so need to skip them both</span></div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;      n--;</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;    }</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;    {</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;      eigen_assert(0 &amp;&amp; <span class="stringliteral">&quot;Internal bug in EigenSolver (INF or NaN has not been detected)&quot;</span>); <span class="comment">// this should not happen</span></div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;    }</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  }</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160; </div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;  <span class="comment">// Back transformation to get eigenvectors of original matrix</span></div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = size-1; j &gt;= 0; j--)</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;  {</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;    m_tmp.noalias() = m_eivec.leftCols(j+1) * m_matT.col(j).segment(0, j+1);</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;    m_eivec.col(j) = m_tmp;</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;  }</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;}</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160; </div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160; </div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_EIGENSOLVER_H</span></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html"><div class="ttname"><a href="classEigen_1_1EigenSolver.html">Eigen::EigenSolver</a></div><div class="ttdoc">Computes eigenvalues and eigenvectors of general matrices.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:67</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a066f584d04b0b8ef1411e3eea9cda7f2"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a066f584d04b0b8ef1411e3eea9cda7f2">Eigen::EigenSolver::Scalar</a></div><div class="ttdeci">MatrixType::Scalar Scalar</div><div class="ttdoc">Scalar type for matrices of type MatrixType.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:82</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a0ccaeb4f7d44c18af60a7b3a1dd91f7a"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a0ccaeb4f7d44c18af60a7b3a1dd91f7a">Eigen::EigenSolver::EigenSolver</a></div><div class="ttdeci">EigenSolver(const EigenBase&lt; InputType &gt; &amp;matrix, bool computeEigenvectors=true)</div><div class="ttdoc">Constructor; computes eigendecomposition of given matrix.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:149</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a0f507ad7ab14797882f474ca8f2773e7"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a0f507ad7ab14797882f474ca8f2773e7">Eigen::EigenSolver::eigenvalues</a></div><div class="ttdeci">const EigenvalueType &amp; eigenvalues() const</div><div class="ttdoc">Returns the eigenvalues of given matrix.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:246</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a311f148c5d12ecda1eec61e31ea8c3ed"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a311f148c5d12ecda1eec61e31ea8c3ed">Eigen::EigenSolver::EigenSolver</a></div><div class="ttdeci">EigenSolver(Index size)</div><div class="ttdoc">Default constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:123</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a4979eafe0aeef06b19ada7fa5e19db17"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a4979eafe0aeef06b19ada7fa5e19db17">Eigen::EigenSolver::pseudoEigenvalueMatrix</a></div><div class="ttdeci">MatrixType pseudoEigenvalueMatrix() const</div><div class="ttdoc">Returns the block-diagonal matrix in the pseudo-eigendecomposition.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:326</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a5c28d646d456a22a2726f49e4e5e8536"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a5c28d646d456a22a2726f49e4e5e8536">Eigen::EigenSolver::info</a></div><div class="ttdeci">ComputationInfo info() const</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:283</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a5fbbdf49cf33b52b1c581bf06319bb91"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a5fbbdf49cf33b52b1c581bf06319bb91">Eigen::EigenSolver::setMaxIterations</a></div><div class="ttdeci">EigenSolver &amp; setMaxIterations(Index maxIters)</div><div class="ttdoc">Sets the maximum number of iterations allowed.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:290</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a66288022802172e3ee059283b26201d7"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a66288022802172e3ee059283b26201d7">Eigen::EigenSolver::eigenvectors</a></div><div class="ttdeci">EigenvectorsType eigenvectors() const</div><div class="ttdoc">Returns the eigenvectors of given matrix.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:347</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a789af79c9427e6617fa8cbd96a6a258e"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a789af79c9427e6617fa8cbd96a6a258e">Eigen::EigenSolver::ComplexScalar</a></div><div class="ttdeci">std::complex&lt; RealScalar &gt; ComplexScalar</div><div class="ttdoc">Complex scalar type for MatrixType.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:92</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a85cf52711e7100b01fda3e329eb86e5e"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a85cf52711e7100b01fda3e329eb86e5e">Eigen::EigenSolver::EigenSolver</a></div><div class="ttdeci">EigenSolver()</div><div class="ttdoc">Default constructor.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:115</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a97733b9f7b4a2cc4496d4066e320c50c"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a97733b9f7b4a2cc4496d4066e320c50c">Eigen::EigenSolver::EigenvalueType</a></div><div class="ttdeci">Matrix&lt; ComplexScalar, ColsAtCompileTime, 1, Options &amp;~RowMajor, MaxColsAtCompileTime, 1 &gt; EigenvalueType</div><div class="ttdoc">Type for vector of eigenvalues as returned by eigenvalues().</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:99</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a9d3d4fb53bbfeb9e96e0f150471a0e81"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a9d3d4fb53bbfeb9e96e0f150471a0e81">Eigen::EigenSolver::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:84</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_a9e03d09fd7cfc0120847fcb63aa353f3"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#a9e03d09fd7cfc0120847fcb63aa353f3">Eigen::EigenSolver::compute</a></div><div class="ttdeci">EigenSolver &amp; compute(const EigenBase&lt; InputType &gt; &amp;matrix, bool computeEigenvectors=true)</div><div class="ttdoc">Computes eigendecomposition of given matrix.</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_ac306853588d05e71d5c0f883d37327f2"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#ac306853588d05e71d5c0f883d37327f2">Eigen::EigenSolver::pseudoEigenvectors</a></div><div class="ttdeci">const MatrixType &amp; pseudoEigenvectors() const</div><div class="ttdoc">Returns the pseudo-eigenvectors of given matrix.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:201</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_acfebb3f08831cb923511dad5a6e78401"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#acfebb3f08831cb923511dad5a6e78401">Eigen::EigenSolver::getMaxIterations</a></div><div class="ttdeci">Index getMaxIterations()</div><div class="ttdoc">Returns the maximum number of iterations.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:297</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_ae1f52c25907e5f00abe236be002eeb89"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#ae1f52c25907e5f00abe236be002eeb89">Eigen::EigenSolver::EigenvectorsType</a></div><div class="ttdeci">Matrix&lt; ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime &gt; EigenvectorsType</div><div class="ttdoc">Type for matrix of eigenvectors as returned by eigenvectors().</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:106</div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html_af54c1d4e3e7faec5c1550056b7549fb7"><div class="ttname"><a href="classEigen_1_1EigenSolver.html#af54c1d4e3e7faec5c1550056b7549fb7">Eigen::EigenSolver::MatrixType</a></div><div class="ttdeci">MatrixType_ MatrixType</div><div class="ttdoc">Synonym for the template parameter MatrixType_.</div><div class="ttdef"><b>Definition:</b> EigenSolver.h:71</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix&lt; ComplexScalar, ColsAtCompileTime, 1, Options &amp;~RowMajor, MaxColsAtCompileTime, 1 &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_a992d58b5453e441dcfc80f21c2bfd1d7"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#a992d58b5453e441dcfc80f21c2bfd1d7">Eigen::PlainObjectBase::coeffRef</a></div><div class="ttdeci">Scalar &amp; coeffRef(Index rowId, Index colId)</div><div class="ttdef"><b>Definition:</b> PlainObjectBase.h:187</div></div>
<div class="ttc" id="aclassEigen_1_1RealSchur_html_a10f9307a8dc2259c86e6dba0edbde308"><div class="ttname"><a href="classEigen_1_1RealSchur.html#a10f9307a8dc2259c86e6dba0edbde308">Eigen::RealSchur::setMaxIterations</a></div><div class="ttdeci">RealSchur &amp; setMaxIterations(Index maxIters)</div><div class="ttdoc">Sets the maximum number of iterations allowed.</div><div class="ttdef"><b>Definition:</b> RealSchur.h:208</div></div>
<div class="ttc" id="aclassEigen_1_1RealSchur_html_a57eea8f6a25be4ac710097fd6cce9366"><div class="ttname"><a href="classEigen_1_1RealSchur.html#a57eea8f6a25be4ac710097fd6cce9366">Eigen::RealSchur::getMaxIterations</a></div><div class="ttdeci">Index getMaxIterations()</div><div class="ttdoc">Returns the maximum number of iterations.</div><div class="ttdef"><b>Definition:</b> RealSchur.h:215</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:442</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">Eigen::NumericalIssue</a></div><div class="ttdeci">@ NumericalIssue</div><div class="ttdef"><b>Definition:</b> Constants.h:446</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_aba24ec81dec745a00b7f33adead89811"><div class="ttname"><a href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">Eigen::isfinite</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isfinite_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isfinite(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a2d768a9877f5f69f49432d447b552bfe"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">Eigen::EigenBase::cols</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:65</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::EigenBase::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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